Radio frequency (RF) and microwave amplifiers, as well as other non-linear devices, are common stages of nearly all types of modern communications systems, such as cell phones. Non-linear devices generate spurious and unwanted products (referred to as “spurious responses”). An input signal may include multiple carriers (or tones), each of which has a corresponding center frequency. The larger number of carriers, the greater the number of spurious responses generated by the non-linear device. The spurious responses include intermodulation disturbances between the carriers, which may be referred to as “intermods,” including interactions among the harmonics of the carriers.
FIG. 1 includes two graphs showing the effects of a non-linear amplifier on multiple carriers. Referring to FIG. 1, spectral input 110 includes two input carriers 111 and 112, which are inputs to non-linear amplifier 120. The non-linear amplifier 120 generates spectral output 130, which includes two amplified carriers 131 and 132 at the same frequencies as the input carriers 111 and 112 but having greater amplitudes (from the amplification). The spectral output 130 also includes intermods 141-149 from 2nd and 3rd order intermodulation distortions (referred to as 2nd and 3rd order intermods), which are the products of the simultaneous amplification of the input carriers 111 and 112 in a non-linear device.
FIG. 2 is a similar graph showing the effects of a non-linear amplifier on ten input carriers. Referring to FIG. 2, spectral output 230 includes the ten amplified carriers, collectively indicated by reference number 231, resulting from ten corresponding input carriers (not shown), respectively. The spectral output 230 also includes two representative sets of 3rd order intermods. First intermod set 241 corresponds to intermod combination (1, 1, −1) and second intermod set 242 corresponds to intermod combination (2, −1). The intermods of the first intermod set 241 may be totaled to provide first intermod envelope 243, and the intermods of the second intermod set 242 may be totaled to provide second intermod envelope 244. Other intermod combinations of the 3rd order intermods (not shown in FIG. 2) include intermod combination (3), intermod combination (2, 1), and intermod combination (1, 1, 1), discussed below.
Notably, the spectral output 230 is only a small bandwidth of the entire output spectra. For clarity, the spectra near DC and all harmonics are not shown. Furthermore, the representative intermods are only due to 3rd order intermodulation distortions, as mentioned above. Higher orders will create more intermods. The intermod combination (1, 1, −1) includes 3rd order intermods generated due to three carriers (or tones) Fi+Fj−Fk, where F is a carrier frequency, i≠j and j≠k. The intermod combination (2, −1) includes 3rd order intermods from two carriers 2Fi−Fj, where i≠j. Multiple intermods appear at the same frequency, which is difficult to illustrate in FIG. 2. In the cable TV industry, for example, the total number of each of these single intermods at the same frequency is referred to as a total number of beats. Each single intermod will have that same amplitude if the frequency response of the amplifier is constant. Also, the amplitude of each of the first and second intermod envelopes 243 and 244 is maximum in the center of the band. In the cable TV industry, the 3rd order intermod combination (1, 1, −1) is referred to as Carrier Triple Beats (CTB). Multiple intermods also appear at the same frequency. The total intermod level in the depicted example will be the sum of both the intermods from 3 tones (1, 1, −1) and 2 tones (2, −1).
Simulating large numbers of intermods is challenging due to the large amount of data created even for low order intermodulation distortions. Simulation time may be long, and quickly becomes impractical using conventional intermod simulation techniques due to large memory requirements, reduced simulation speed and limited display capabilities. Notably, the wireless industry continues to move to higher bandwidths and use more RF carriers. Also, in the cable TV industry, over a hundred channels are being amplified and processed by non-linear stages. These non-linear stages generate intermods that fall in-band as well as out-of-band. Understanding the spurious performance of systems processing hundreds of carriers is important to deliver quality cable TV products to customers.